Exploring the Hodgkin Huxley equations

These famous equations model the squid-axon and are an excellent example of the type of model that one obtains by using the methods of the previous section. The equations are:

where

and

$$\phi = 3^{(T-6.3)/10}$$

corrects for the temperature on the kinetics. The figures below illustrate the kinetic functions and the functions for $m_\infty,\tau_m,$ etc. Note that in all cases the steady state voltage dependence is sigmoidal with n and m monotonically increasing and h decreasing. Also notice that the maximum of the time constant of the sodium activation is about .5 and that of h and n are 8 and 5 respectively. The sodium activation is more than ten times as fast as the inactivation and the delayed rectifier current. Also note that at the activation threshold, the h is nearly zero.